Pastor Armstrong taught it was hard to evangelize certain other religions because thay think their good works get them to Heaven. Isn't it all up to God to determine who is saved? I am a little confused please help.
As your question implied, Scripture teaches that all men are born dead in sin, unable to truly seek God and forever opposed to Him by our nature. Only after God brings about a new spiritual birth will anyone respond in faith. In Romans Paul explains this Biblical reality in careful detail, and he teaches that grace is most clearly understood as the way God brings us to faith while we are lost in our sin.
This fact gives rise to numerous questions. For example, what place does evangelism play in bringing others to faith? Can we influence God's choice in bringing someone to faith? What purpose do our evangelistic efforts serve? Pastor Armstrong teaches on many of these points during the course of his Romans study, but we can summarize them for you here:
First, God is the Author and Perfecter of our faith (Heb 12:2), and as such, He alone is responsible for our salvation. Simply put, men are saved if (and when) God chooses to save them (Eph 2:8-9). Nevertheless, God has purposed to work through the efforts of men to spread the Gospel and bring others to know Him (Matt 28:19-20). The Great Commission is fundamentally an expression of how Christ will build His Church through the work of believers.
If we accept these truths, we come to the conclusion that our participation in spreading the Gospel is intended for God's glory and for our own blessing, yet our participation in evangelism is not essential to God's purposes in saving men nor do we share any of His glory when we participate obediently in bringing others to faith.
Pastor Armstrong often uses an analogy of an Easter egg hunt to explain the relationship between God's sovereignty in salvation and our responsibility to spread the Gospel. In his analogy, Pastor Armstrong describes the unbeliever as an egg hidden in the world waiting for someone to discover it. The Bible says that God the Father sovereignly decides who will receive the Gospel, which may be compared to the way a parent decides how many eggs are available and where they are hidden in the yard.
Our world is littered with hidden "eggs" (i.e., future believers) waiting to be found. We find them by obeying the Great Commission. The Father is constantly working by His Spirit in the world to prepare hearts to receive the Gospel, and these "eggs" are ours for the taking if we seek after them (John 4:35). Like a child who runs around the yard eagerly searching for eggs, we should work eagerly to fulfill Christ's commands so that we might have the opportunity to "discover" the next believer.
When we come across a heart made ready by God's Spirit, we have found an egg, and we will see a positive response to the Gospel (John 6:44). Our enthusiasm to spread the Gospel should stem from our confidence that God has placed hearts in the world ready for the gospel, so we know if we look long enough, we will find success. In this sense, God's sovereignty in salvation is our reason TO evangelize (rather than an excuse NOT to seek the lost), because we have confidence that the "eggs" do exist somewhere.
In the Easter egg hunt, the children don't determine how many eggs exist, but they can influence how many each child may collect. Likewise, we don't determine the souls to be saved by God's grace, but we can influence how many may believe through the diligent practice of our faith, and if we are faithful to seek after these "eggs," we gain the praise and reward of our master for that faithful service.
To summarize, we actively participate in seeking the lost by proclaiming the good news of the Gospel and discipling the saved because our Lord commanded us to do so. We serve Him obediently in these ways in expectation of success because we know He has purposed to work through men to bring the lost to faith, and because we understanding we have opportunity to gain reward for our faithfulness. In the end however, the number who will be saved was determined by God's choice from the foundations of the earth (Eph 1:4).
Lastly, you raised a good point in questioning Pastor's Armstrong's comments regarding his difficulty evangelizing to certain groups. Fundamentally, you are correct that God may choose to save anyone, so no group is outside His will to bring them to faith. Pastor Armstrong didn't intend to suggest that any group is less able to be saved. On the other hand, it is Pastor Armstrong's experience that certain religious groups can be particularly resistant to the Gospel, which may be a reflection of God's desire to leave some in disobedience and ignorance.
Nevertheless, Verse By Verse Ministry is no less committed to delivering the Good News to every person possible, since we do not presume whom the Lord is prepared and willing to grant mercy. Pastor Armstrong continues to teach to any group in the hope that he might discover another "egg" there, and he thanks you for bringing this point to his attention. He intends to correct his presentation on this point in the future.